# What is the derivative of y= (x^2 + 2x + 5) / (x + 1)?

$y = \frac{{x}^{2} + 2 x + 5}{x + 1}$
$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(x + 1\right) \left(2 x + 2\right) - \left({x}^{2} + 2 x + 5\right) \left(1\right)}{x + 1} ^ 2$
$= \frac{2 {x}^{2} + 4 x + 2 - {x}^{2} - 2 x - 5}{x + 1} ^ 2 = \frac{{x}^{2} + 2 x - 3}{x + 1} ^ 2$